What would you guys suggest as a good introduction book to small area estimation?
It seems like the wikipedia article is a reasonable place to start. In particular, if you don't have access to the Rao book (which appears to be the only logical choice for a reference book), one might check out the two review articles cited on wikipedia as well;
It is a contemporary field, so any recent developments will more likely be contained within journal articles than books. One can utilize google scholar and the "cited by feature" to muck through anyone who has cited the Rao book. This in combination with just searching small area estimation is likely to yield a comprehensive list of popular literature on the subject.
If one wants to cast the net alittle bit broader, probably a natural extension to the multi-variate case is examining hierarchical spatial random effects models (Kang et al., 2009). Although these should come up in searches for "small area" anyway. There Noel Cressie's work will be of most interest, and many examples are currently in the public health/epidemiology although other examples in demography, sociology, economics and criminology exist as well (so examples are likely scattered a wide array of journals). I'm a social science guy so I'm ignorant to the extent such examples exist in the natural and environmental sciences. It also may be the case that one of Noel Cressie's book has topical material of interest, although I don't own any so I can't say for sure off-hand.
For completeness, the special issues Stask mentions in the comments;
While searching for any output of the IASS I came across some conferences in Europe entirely devoted to small area estimation, although they don't appear to have a devoted website (see examples for conferences in 2007, 2009, and 2011).
Also I noticed one statistician frequently particpating in those conferences that I had not mentioned so far was Partha Lahiri. Looking at his CV it looks like he is currently writing a book on small area estimation (as well as has a variety of other scholarly material of interest to the topic).